A131086 Triangle read by rows: T(n,k) = 2*binomial(n,k) - (-1)^(n-k) (0 <= k <= n).

1, 3, 1, 1, 5, 1, 3, 5, 7, 1, 1, 9, 11, 9, 1, 3, 9, 21, 19, 11, 1, 1, 13, 29, 41, 29, 13, 1, 3, 13, 43, 69, 71, 41, 15, 1, 1, 17, 55, 113, 139, 113, 55, 17, 1, 3, 17, 73, 167, 253, 251, 169, 71, 19, 1, 1, 21, 89, 241, 419, 505, 419, 241, 89, 21, 1, 3, 21, 111, 329

Offset: 0

Author

Gary W. Adamson, Jun 14 2007

Keywords

• nonn
• tabl

Comments

Row sums = A051049 starting (1, 4, 7, 16, 31, 64, ...).

Examples

			First few rows of the triangle are
  1;
  3,  1;
  1,  5,  1;
  3,  5,  7,  1;
  1,  9, 11,  9,  1;
  3,  9, 21, 19, 11,  1;
  1, 13, 29, 41, 29, 13,  1;
  ...
		

Crossrefs

Cf. A000012, A051049.

Programs

Maple

T := proc (n, k) if k <= n then 2*binomial(n, k)-(-1)^(n-k) else 0 end if end proc: for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 21 2007

Formula

G.f. = G(t,z) = (1 + 3z - tz - 2tz^2)/((1+z)(1-tz)(1-z-tz)). - Emeric Deutsch, Jun 21 2007

Extensions

More terms from Emeric Deutsch, Jun 21 2007

Sequence corrected by N. J. A. Sloane, Sep 30 2007